source.rb

...

private
  def use_dsl(&block)
    proxy = Proxy.new(self, @api)
    proxy.call(&block)
  end
end

class Proxy < BasicObject
  class CallerFrame < BasicObject
    def initialize(receiver)
      @receiver = receiver
    end

    def eval(&block)
      @receiver.instance_exec(&block)
    end
  end

  def initialize(*args)
    @receivers = args
  end

  def call(&block)
    caller_frame = CallerFrame.new(@receivers.first)
    instance_exec(caller_frame, &block)
  end

  def method_missing(method, *args, &block)
    @receivers.each do |receiver|
      return receiver.send(method, *args, &block) if receiver.respond_to?(method, true)
    end
  end
end

# Output:
#
# a: 1
# No method `a`
# b: 2
# No method `b`
# c: nil
# c: 3
# No method `c`